First slide

Work

Question

A body of mass 6kg is under a force which causes displacement in it given by $S = \frac{t^{2}}{4}$ metres where t is time. The work done by the force in 2 seconds is

Moderate

A

12 J
B

9 J
C

6 J
D

3 J

Solution

$s = \frac{t^{2}}{4} ∴ ds = \frac{t}{2} dt$
$F = ma = \frac{{md}^{2} s}{{dt}^{2}} = \frac{6 d^{2}}{{dt}^{2}} [\frac{t^{2}}{4}] = 3 N$
Now
$W = \int_{0}^{2} F ds = \int_{0}^{2} 3 \frac{t}{2} dt = \frac{3}{2} {[\frac{t^{2}}{2}]}_{0}^{2} = \frac{3}{4} [{(2)}^{2} - {(0)}^{2}] = 3 J$

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